I wouldn't bother changing the oil as a first step if the dipstick is showing it being milky. You have bigger problems if you have a blown head gasket, and will have to change the oil again anyway.
The water covers 33" tires ... I don't think iit got to the intake
doubt your air filter got anything in it if it was just over the tires. Depends how hard you hit it though...
Have you checked anything? Or is all you know is there is white smoke?
The tail pipe was under water so I didn't turn off the jeep until I got towed out 3 hours later.
3 hrs in a mud hole with a rad clogged with mud could very well overheat it......
x2
From the sounds of things, you don't know a whole lot about the mechanics under the hood, so take it to a mechanic. Call around and see if they can give you a free quote. At least that way you will know what's wrong with it and have a rough idea how much it's gonna cost you. If the mechanics are like the ones out here, double the price they quote just to be safe.
Or if you have the time, use it as a project to start learning. Youtube videos if you have to, buy a repair manual.
Overall, this should be a good lesson why you should never wheel alone. 3 hours stuck is way to long.